Enhanced 2-categories and limits for lax morphisms

By Stephen Lack, Michael Shulman. 2011

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Abstract We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or may not be required to be invertible. This is done using the framework of 2-monads. In order to characterize the limits which exist in this context, we need to consider also the functors which do strictly preserve the extra structure. We show how such a 2-category of weak morphisms which is “enhanced”, by specifying which of these weak morphisms are actually strict, can be thought of as category enriched over a particular base cartesian closed category F . We give a complete characterization, in terms of F -enriched category theory, of the limits which exist in such 2-categories of categories with extra structure.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/4f47f7854844f5d265614c81e9e84a21b7cb4f6d

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Citations in the corpus

Enriched categories as a free cocompletion (2013, methodology): “As in [23], we call such an equipment inchordate.”